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arXiv · 1710.03173

Local-Global Principles for Zero-Cycles on Homogeneous Spaces over Arithmetic Function Fields

Jean-Louis Colliot-Thélène·David Harbater·Julia Hartmann·Daniel Krashen·R. Parimala·V. Suresh
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Abstract

We study the existence of zero-cycles of degree one on varieties that are defined over a function field of a curve over a complete discretely valued field. In particular, we show that local-global principles hold for such zero-cycles provided that local-global principles hold for the existence of rational points over extensions of the function field. This assertion is analogous to a known result concerning varieties over number fields. We also show that our results hold more generally in the henselian case.

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Jean-Louis Colliot-Thélène, David Harbater, Julia Hartmann, Daniel Krashen, R. Parimala, V. Suresh. 2017-10-09. Local-Global Principles for Zero-Cycles on Homogeneous Spaces over Arithmetic Function Fields. https://arxiv.org/abs/1710.03173

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